THE ESTIMATION OF SPECTRUM, INVERSE SPECTRUM AND INVERSE AUTOCOVARIANCES OF A STATIONARY TIME SERIES

T. Subba Rao and M. M. Gabr

Journal of Time Series Analysis, 1989, vol. 10, issue 2, 183-202

Abstract: Abstract. In this paper we consider the method of spectral estimation proposed by Pisarenko, and interpret its form through the properties of circular symmetric matrices. This interpretation helps us to redefine Capon's ‘high resolution’ estimation for time series defined on the real line. Using the properties of the eigenvalues and eigenvectors of Wishart matrices, we study the sampling properties of these matrices, applying a method of derivation different from that given by Pisarenko. We also show how Capon's high resolution estimator can be used to estimate the inverse spectrum and the inverse autocovariances, and we derive the asymptotic sampling properties of these estimates. The methods are illustrated with examples.

Date: 1989
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